Everyone from the president to the lawmakers who are supposed to oversee the National Security Agency claim they had no idea it was spying on the communications of dozens of foreign leaders. But that claim is laughable, according to veteran members of the intelligence community, former White House advisers, and now one of the NSA’s main overseers in Congress.

A former White House official, who served in a prior administration, said it was essentially impossible that the president wouldn’t know foreign leaders were being monitored by U.S. intelligence agencies, and principally the NSA, as part of regular operations aimed at keeping him informed about diplomatic relations and negotiations. Information on foreign leaders that is based on recorded calls or other signals intelligence is "unique," the former official said, and its nature is obvious to anyone reading or hearing an intelligence report or receiving a briefing.

"If you saw it, you’d know that it came out of somebody’s mouth," the former official said. "I cannot believe that [Obama’s national security staff] didn’t brief the president on foreign leaders when he was going in to visit with them." Much of that information would have comes from signals intelligence. And the failure to inform the president that a piece of information came from spying on a leader could be a fireable offense, the former White House official said. "It’s almost a dereliction not to tell him."

At a hearing Tuesday about whether to modify current surveillance law that governs the NSA’s activities, a clearly frustrated Mike Rogers, the chairman of the House Intelligence Committee, all but admitted that the NSA had revealed to members of his committee the details of an operation that targeted the personal communications of as many as 35 heads of state and government. And if his colleagues didn’t know it, Rogers implied, they weren’t paying attention.

Rogers said the committee is privy to huge amount of information on U.S. spying, including a list of priority intelligence topics that is approved and modified by the president and his advisers and sets out the parameters of U.S. intelligence gathering. And, he said, committee members have access to "sources and methods" of spying, as well as "mounds of material" about the fruits of intelligence.

In a testy exchange with Rep. Adam Schiff, a California Democrat who questioned why the committee had not been informed that the NSA had intercepted the phone calls of German Chancellor Angela Merkel, Rogers fired back that the committee had been kept in the loop and that if Schiff hadn’t read the reports he had no one to blame but himself.

"To make the case that somehow we are in the dark is mystifying to me," Rogers said. "Some members spend a lot more time on this committee than others based on their schedules, which are significant in this Congress. But it is disingenuous to imply that this committee did not have a full and complete understanding of activities of the intelligence community."

Asked directly by Schiff whether he was aware that the NSA had targeted the phone calls of foreign leaders, Rogers refused to confirm a specific operation but emphasized that "we have access to all sources and methods, and there is lots of product to be reviewed by the intelligence committee."

"We would be happy to take you down to the committee and spend a couple of hours going through mounds of product that would allow a member to be as informed as a member wishes to be on sources and methods," a clearly frustrated Rogers told Schiff.

Asked if Rogers had just confirmed knowledge of the NSA operations spying on foreign leaders, a spokesperson said, "The chairman’s comment speaks for itself."

Former government officials with long experience in the intelligence community said they doubted that President Obama didn’t have some idea that Merkel’s and other leaders’ communications were being monitored in some capacity, even if he didn’t know the specifics of those operations.

President Obama doesn’t approve particular methods of surveillance or select its targets, and his daily intelligence briefing is filled with more reports on national security threats — such as terrorism or Iran’s nuclear program — than it is information about allies.

"As a general matter, it’s not reasonable to expect that the president would have been involved in or necessarily briefed on decisions about individual intelligence targets; rather, he approves a set of intelligence priorities, and then it’s the responsibility of his administration to determine how to carry those out," said a senior administration official.

At the hearing, Rep. Michele Bachmann asked intelligence officials to what extent the White House is kept informed of surveillance operations such as the one that targeted Merkel. James Clapper, the director of national intelligence, said that National Security Council officials responsible for a particular country are typically informed of operations in their area of responsibility. Pressed by Bachmann whether intelligence reports presented to the president and his staff might include sourcing information that would have made them aware that Merkel’s phone was being tapped, Clapper claimed that it would be "unlikely and unrealistic" that the reports would go into the level of detail to reveal sources.

But the provenance of the intelligence the president receives is not a mystery. "[Obama] doesn’t have time to get a briefing on every aspect" of NSA intelligence gathering, said a former U.S. government official. "But Merkel is someone he talks to and meets with regularly. There’s no way that before a call, say in advance of a G8 meeting, he’s not going to ask his national security adviser, ‘What’s Merkel’s position?’"

And when a president asks such a question, he doesn’t expect his advisers to speculate. He wants to know what information they’ve received from the intelligence agencies, among other sources.

It’s also unlikely that foreign officials were surprised to learn that their communications were being monitored by the United States. Foreign leaders have reacted with a mix of offense and outrage to revelations of NSA spying. In Germany, protesters have marched in the streets, and Merkel personally called Obama to express her anger at having her phone tapped.

But there is an element of theater in these protests.

"A lot of what I believe the Europeans are publicly saying about this is mostly for their public support. I think they want their people to have an understanding that they’re infuriated," said Bob Stasio, a former intelligence community official. "There’s no doubt in my mind that those folks in those positions know everything is fair game. This is what countries do."

As for professed outrage among some U.S. officials, Stasio called it "a microcosm of the European reaction. I can’t say they were specifically aware of which people were targeted. But they had to have some idea conceptually that this was going on. That’s what the [NSA] is authorized to do," said Stasio, now the CEO of Ronin Analytics, a cybersecurity company.

In light of that reality, intelligence experts were especially mystified by a scathing rebuke of the NSA issued yesterday by one of its staunchest defenders, Sen. Dianne Feinstein, the chairman of the Senate Intelligence Committee. Feinstein said she was "totally opposed" to spying on U.S. allies and was outraged to learn it had been happening for more than a decade.

"Don’t get me started on that," said another former U.S. government official who is deeply familiar with intelligence issues, adding that Feinstein, who is privy to classified intelligence reports, should have known where the information was coming from. "It’s as if your spouse shows up with a big bag of money and it never occurs to you to ask: ‘Hey, I wonder how he got all this cash," the former official said. "She’s not doing it in bad faith. It just never dawned on her, apparently. Except, how long has she been chairman now?"

It was "certainly plausible" that Obama didn’t know specifically about the NSA tapping Merkel’s phone, the former official said. "It’s one thing to recognize that certain types of collection are taking place. It’s another to understand their scale and scope." But, the former official continued, "Ask yourself this: Do you think the French try to spy on President Obama? Of course they do! We presume he’s a target to friendly and hostile nations alike — any country with an intelligence apparatus."

The senior administration official, without specifying details about who knew what and when, said that Obama "feels strongly about making sure that we are collecting information not just because we can, but because we should."

As for signals intelligence, and where it fits into the mix, the official said it was just one piece. The president doesn’t rely solely on that source, and in the case of allies, information used to prepare him for meeting with leaders "comes mostly from the fact that we have regular and frank interactions with our counterparts every day through our embassy and from here. We know what they are thinking because we talk to them about it."